Normal families concerning partially shared and proximate values

Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ hav...
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Autor*in:	Kumar, Rahul [verfasserIn] Bharti, Nikhil

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Normal families Partially shared values Partially proximate values Meromorphic functions

Anmerkung:	© Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: São Paulo journal of mathematical sciences - [Cham, Switzerland] : Springer International Publishing, 2015, 17(2022), 2 vom: 29. Sept., Seite 1076-1085
Übergeordnetes Werk:	volume:17 ; year:2022 ; number:2 ; day:29 ; month:09 ; pages:1076-1085

Links:	Volltext

DOI / URN:	10.1007/s40863-022-00341-9

Katalog-ID:	SPR05401879X

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520			\|a Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.)
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650		4	\|a Partially shared values \|7 (dpeaa)DE-He213
650		4	\|a Partially proximate values \|7 (dpeaa)DE-He213
650		4	\|a Meromorphic functions \|7 (dpeaa)DE-He213
700	1		\|a Bharti, Nikhil \|0 (orcid)0000-0003-2501-6247 \|4 aut
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allfields	10.1007/s40863-022-00341-9 doi (DE-627)SPR05401879X (SPR)s40863-022-00341-9-e DE-627 ger DE-627 rakwb eng Kumar, Rahul verfasserin aut Normal families concerning partially shared and proximate values 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) Normal families (dpeaa)DE-He213 Partially shared values (dpeaa)DE-He213 Partially proximate values (dpeaa)DE-He213 Meromorphic functions (dpeaa)DE-He213 Bharti, Nikhil (orcid)0000-0003-2501-6247 aut Enthalten in São Paulo journal of mathematical sciences [Cham, Switzerland] : Springer International Publishing, 2015 17(2022), 2 vom: 29. Sept., Seite 1076-1085 (DE-627)843637404 (DE-600)2842503-0 2316-9028 nnns volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085 https://dx.doi.org/10.1007/s40863-022-00341-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2022 2 29 09 1076-1085
spelling	10.1007/s40863-022-00341-9 doi (DE-627)SPR05401879X (SPR)s40863-022-00341-9-e DE-627 ger DE-627 rakwb eng Kumar, Rahul verfasserin aut Normal families concerning partially shared and proximate values 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) Normal families (dpeaa)DE-He213 Partially shared values (dpeaa)DE-He213 Partially proximate values (dpeaa)DE-He213 Meromorphic functions (dpeaa)DE-He213 Bharti, Nikhil (orcid)0000-0003-2501-6247 aut Enthalten in São Paulo journal of mathematical sciences [Cham, Switzerland] : Springer International Publishing, 2015 17(2022), 2 vom: 29. Sept., Seite 1076-1085 (DE-627)843637404 (DE-600)2842503-0 2316-9028 nnns volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085 https://dx.doi.org/10.1007/s40863-022-00341-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2022 2 29 09 1076-1085
allfields_unstemmed	10.1007/s40863-022-00341-9 doi (DE-627)SPR05401879X (SPR)s40863-022-00341-9-e DE-627 ger DE-627 rakwb eng Kumar, Rahul verfasserin aut Normal families concerning partially shared and proximate values 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) Normal families (dpeaa)DE-He213 Partially shared values (dpeaa)DE-He213 Partially proximate values (dpeaa)DE-He213 Meromorphic functions (dpeaa)DE-He213 Bharti, Nikhil (orcid)0000-0003-2501-6247 aut Enthalten in São Paulo journal of mathematical sciences [Cham, Switzerland] : Springer International Publishing, 2015 17(2022), 2 vom: 29. Sept., Seite 1076-1085 (DE-627)843637404 (DE-600)2842503-0 2316-9028 nnns volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085 https://dx.doi.org/10.1007/s40863-022-00341-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2022 2 29 09 1076-1085
allfieldsGer	10.1007/s40863-022-00341-9 doi (DE-627)SPR05401879X (SPR)s40863-022-00341-9-e DE-627 ger DE-627 rakwb eng Kumar, Rahul verfasserin aut Normal families concerning partially shared and proximate values 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) Normal families (dpeaa)DE-He213 Partially shared values (dpeaa)DE-He213 Partially proximate values (dpeaa)DE-He213 Meromorphic functions (dpeaa)DE-He213 Bharti, Nikhil (orcid)0000-0003-2501-6247 aut Enthalten in São Paulo journal of mathematical sciences [Cham, Switzerland] : Springer International Publishing, 2015 17(2022), 2 vom: 29. Sept., Seite 1076-1085 (DE-627)843637404 (DE-600)2842503-0 2316-9028 nnns volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085 https://dx.doi.org/10.1007/s40863-022-00341-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2022 2 29 09 1076-1085
allfieldsSound	10.1007/s40863-022-00341-9 doi (DE-627)SPR05401879X (SPR)s40863-022-00341-9-e DE-627 ger DE-627 rakwb eng Kumar, Rahul verfasserin aut Normal families concerning partially shared and proximate values 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) Normal families (dpeaa)DE-He213 Partially shared values (dpeaa)DE-He213 Partially proximate values (dpeaa)DE-He213 Meromorphic functions (dpeaa)DE-He213 Bharti, Nikhil (orcid)0000-0003-2501-6247 aut Enthalten in São Paulo journal of mathematical sciences [Cham, Switzerland] : Springer International Publishing, 2015 17(2022), 2 vom: 29. Sept., Seite 1076-1085 (DE-627)843637404 (DE-600)2842503-0 2316-9028 nnns volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085 https://dx.doi.org/10.1007/s40863-022-00341-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 17 2022 2 29 09 1076-1085
language	English
source	Enthalten in São Paulo journal of mathematical sciences 17(2022), 2 vom: 29. Sept., Seite 1076-1085 volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085
sourceStr	Enthalten in São Paulo journal of mathematical sciences 17(2022), 2 vom: 29. Sept., Seite 1076-1085 volume:17 year:2022 number:2 day:29 month:09 pages:1076-1085
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Normal families Partially shared values Partially proximate values Meromorphic functions
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container_title	São Paulo journal of mathematical sciences
authorswithroles_txt_mv	Kumar, Rahul @@aut@@ Bharti, Nikhil @@aut@@
publishDateDaySort_date	2022-09-29T00:00:00Z
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author	Kumar, Rahul
spellingShingle	Kumar, Rahul misc Normal families misc Partially shared values misc Partially proximate values misc Meromorphic functions Normal families concerning partially shared and proximate values
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topic_title	Normal families concerning partially shared and proximate values Normal families (dpeaa)DE-He213 Partially shared values (dpeaa)DE-He213 Partially proximate values (dpeaa)DE-He213 Meromorphic functions (dpeaa)DE-He213
topic	misc Normal families misc Partially shared values misc Partially proximate values misc Meromorphic functions
topic_unstemmed	misc Normal families misc Partially shared values misc Partially proximate values misc Meromorphic functions
topic_browse	misc Normal families misc Partially shared values misc Partially proximate values misc Meromorphic functions
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title	Normal families concerning partially shared and proximate values
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title_full	Normal families concerning partially shared and proximate values
author_sort	Kumar, Rahul
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author_browse	Kumar, Rahul Bharti, Nikhil
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author-letter	Kumar, Rahul
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title_sort	normal families concerning partially shared and proximate values
title_auth	Normal families concerning partially shared and proximate values
abstract	Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.) © Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Normal families concerning partially shared and proximate values
url	https://dx.doi.org/10.1007/s40863-022-00341-9
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author2	Bharti, Nikhil
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doi_str	10.1007/s40863-022-00341-9
up_date	2024-07-03T23:29:52.851Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR05401879X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231208064702.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231208s2022 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40863-022-00341-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR05401879X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40863-022-00341-9-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kumar, Rahul</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Normal families concerning partially shared and proximate values</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Instituto de Matemática e Estatística da Universidade de São Paulo 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we discuss normality of two families of meromorphic functions concerning partially shared values. Precisely, we proved: Let %${\mathcal {F}}%$ and %${\mathcal {G}}%$ be two families of meromorphic functions on a domain D such that all zeros of each %$f\in {\mathcal {F}}%$ have multiplicities at least %$k+1,%$ where %$k\ge 1%$ is an integer and let a, b and c be three finite distinct complex numbers. Assume that %${\mathcal {G}}%$ is normal in D and for each %$f\in {\mathcal {F}},%$ there exists %$g\in {\mathcal {G}}%$ such that a, b, c are partially shared values of %$f^{(k)}%$ and g. Then %${\mathcal {F}}%$ is normal in D. We also give examples to show that various conditions in the hypothesis of this theorem cannot be weakened. Furthermore, we introduce a notion of proximate values of meromorphic functions and obtain some normality criteria involving partially proximate values which generalize an established result of Liu, Li and Pang (Acta Math Sinica English series 29 (1) (2013), 151-158.)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Normal families</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Partially shared values</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Partially proximate values</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Meromorphic functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bharti, Nikhil</subfield><subfield code="0">(orcid)0000-0003-2501-6247</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">São Paulo journal of mathematical sciences</subfield><subfield code="d">[Cham, Switzerland] : Springer International Publishing, 2015</subfield><subfield code="g">17(2022), 2 vom: 29. Sept., Seite 1076-1085</subfield><subfield code="w">(DE-627)843637404</subfield><subfield code="w">(DE-600)2842503-0</subfield><subfield code="x">2316-9028</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:17</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:2</subfield><subfield code="g">day:29</subfield><subfield code="g">month:09</subfield><subfield code="g">pages:1076-1085</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s40863-022-00341-9</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield 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